I broke down last weekend and bought a Renzetti traveller last weekend to replace a cheap, worn out, vise. When tying with it I realized that I need to rethink how I tie to take advantage of the rotary feature. My questions are:

What do I do with the bobbin rest? I hit it on every wrap of thread until I took it off.

Besides inspecting the back side of a fly, what steps should I use the rotary feature for?

The bobbin rest should be able to be pushed out of the way when not in use. I use the rotary feature to help me more evenly attach materials, to apply epoxy and other stuff more easily, and to wrap materials like chenile and dubbing.

I'm sure there are a number of other functions but..
The bobbin rest is best used when you are palmering hackle or zonker and/or wrapping material on the hook shank like dubbing, body braid or tinsel. The key it to have the shank of the hook on the same centerline as the axis of the vise, then position the bobbin rest so that the thread tracks right at the eye of the hook.
Some tiers will use the rotary function when applying the threads to the hook but I find it's faster to rotate the bobbin tip.
As Greg says, just swing it back 90* when you don't need it. Never in the way back there.
Other functions;
It's often easier to build a lower wing/body of a fly with the hook inverted, doing a high/low tie on a fly you are always reversing position.
I find it very helpful in matching location when applying eyes.
Building epoxy heads when using quick-dry epoxy

[by the time I finished my reply Bob provided a much more concise summary - read this if you have spare time ]

The bobbin rest is very useful if you are doing (for lack of better term) multi-level tying operations. What the heck does that mean?

Let's start with a wolly bugger. Everyone ties 'em sooner or later. It has a palmered hackle over chenille. On a stationary vise, both are wound around and around the hook shaft. The results can be (but not always) uneven and it's not easy to re-wrap to straighten, especially because you want the stem to be against the chenille with the barbs pointing outward with no twisting of the hackle. Wrapping the hand around the hook inherently twists the feather. That's why people make and buy expensive universal hackle pliers that hinge at the union of handle and jaws... to provide the degree of freedom to keep a feather straight during the winding process.

With rotary, you hold the feather in the desired position and turn the fly. It can't twist unless you go out of your way to twist it. I haven't used the universal hackle pliers in years, they don't even make it in my main tying kit anymore. If you screw it up (unevenly wound) on the rotary, you unwind and wrap it again in two seconds.

But that doesn't answer the question... the bobbin holder pivots on the vise shaft, and tilts on it's own shaft axis too. I swing the holder to the front (away from me) while wrapping stuff, and swing it in when I need it to hold the bobbin.

When do you need to hold the bobbin?

Let's go back to the wolly bugger. After tying in the hackle at the front of the fly, you've completed the chenille body by spinning the fly hook while holding the chenille like a lathe bit. Pc of cake. Now, you tie down the end of the chenille using a whip finish, I prefer the matarelli tool, some prefer their fingers. I can do both but the tool is so much easier for me (results may vary).

Swing the bobbin arm closer so it is in-line with the fly shaft, and lay the thread coming from the whipped chenille (near the bend of the hook) onto the arm. Now you can take your hands off everything and grab the hackle that winds over the chenille. Hold it flat against the chenille and turn the rotary vise, laying the feather on the chenille in a spiral toward the tail as the fly spins. The thread and bobbin are held by the arm and thus does not dangle, twist or wrap during this step... because the thread lies in the same axis as the hook while spinning.

Now that the hackle has been wound to the spot where the thread was whipped in place, you can now pick up the bobbin and wrap the feather in place. even if you preferred to tie in the marabou first, the thread and the marabou would be in-line and spinning with each other so would not tangle during the hackle wrap.

Once again, some tie circles around me with a fixed vise. Your results may vary.

A wooly bugger, interesting choice for a description. It's a great fly, tie some in large sizes 4/0 chartreus is my favorite, but yellow and white also work, and throw them at stripers and blues... You won't be sorry.

I just picked up the Saltwater Traveler myself. Got to admit I like it, especially for keeping track of material distribution. Also, I need all the help I can get. If I were Native American my name would be Ten Thumbs. Too many jambed knuckles from basketballs off the fingertips during my gym rat days.

I started tying about 8 weeks ago and went with the Renzetti traveler and really can not compare it to anything else but I am very satisfied and the rotary feature was the way to go for me... made the learning curve shorter and there is nothing like it for epoxy application.. Also, I was convinced to get the regular traveler instead of the saltwater since I could do trout flies sometime in the future. I have tied 4/0 hooks easily down to size 4 for saltwater... that about covers it for me.

I saw Lefty tying wooly buggers on a tape. he called em indestructable wooly buggers. he takes 2 strips of chennile and achors them down with the hackle between them in the hackle pliers, spins it a bit , then winds it up the shank... tada!!! done Tom D

With a rotary vise, another method to make the chennile and hackle rope instead of twisting the hackle plier is:
1. anchor chennile and hackle at the tail tie in point
2. wrap your thread to just behind the hook eye and half hitch there and lay thread over bobbin holder
3. grasp the chennile and hackle in hackle pliers and hold them horizontally along the hook shank
4. rotate the vise until you have the desired rope
5. move the rope towards you until it is perpendicular to the hook shank
6. rotate the vise to place chennile and hackle rope onto the hook shank.

This sounds like a lot of detail, but give a try it really moves fast about the second time you do it...